Resumo O argumento do Terceiro Homem presente no “Parmênides” constitui uma formidável objeção à teoria das Ideias, à qual Platão não apresentou resposta explícita. A despeito disso, cremos ser possível haurir da filosofia platônica uma solução para a referida objeção, solução esta que estaria verossimilmente à disposição do filósofo. Sendo assim, compreende-se que Platão não tenha sido forçado a renunciar à teoria das Ideias, ao menos no que se refere às dificuldades que o Terceiro Homem lhe opõe.The Third Man Argument (...) presented in the “Parmenides” is a formidable objection to the Theory of Forms, one which Plato did not provide an explicit answer to. In spite of that we believe it is possible to draw from Plato’s philosophy a solution to the referred objection, and one which likely would be available to the philosopher. Thus, it becomes clear that Plato was not forced to renounce his Theory of Forms, at least with regard to the difficulties that the Third Man Argument raises to it. (shrink)

La exposición y crítica de las doctrinas antiguas tiene un lugar importante en los escritos de Aristóteles. Sin embargo, ciertas dudas se han vuelto corrientes acerca de la confiabilidad de sus descripciones. Más aún, se ha sostenido que Aristóteles deforma la comprensión histórica a través de la introducción de conceptos y términos propios. En este libro se aborda el problema a través de un análisis de las críticas que Aristóteles dirige a la teoría platónica de las Ideas, que permite explicar (...) la constitución y desarrollo de importantes conceptos aristotélicos a partir de la confrontación dialéctica con las doctrinas de su maestro. En efecto, las dificultades genuinas que Aristóteles descubre en el platonismo constituyen el motor para gestar nuevos conceptos, que no son ajenos, sino que surgen como implicaciones del examen crítico. Así, la imposición de términos propios no debe interpretarse como distorsión, sino como el modo que Aristóteles adopta para exhibir su particular solución a los problemas que los filósofos anteriores dejaron sin solución. (shrink)

In this book, Zalta attempts to lay the axiomatic foundations of metaphysics by developing and applying a (formal) theory of abstract objects. The cornerstones include a principle which presents precise conditions under which there are abstract objects and a principle which says when apparently distinct such objects are in fact identical. The principles are constructed out of a basic set of primitive notions, which are identified at the end of the Introduction, just before the theorizing begins. The main reason for (...) producing a theory which defines a logical space of abstract objects is that it may have a great deal of explanatory power. It is hoped that the data explained by means of the theory will be of interest to pure and applied metaphysicians, logicians and linguists, and pure and applied epistemologists. (shrink)

In this paper I investigate the relation between physics and metaphysics in Plato’s participation theory. I show that the logic shoring up Plato’s metaphysics in paraconsistent, as had been suggested already by Graham Priest. The transformation of the paradoxical One-and-Many of the pre-Socratics into a paraconsistent Great-and-Small bridges the abyss between archaic rationality and the world of classical logic based ultimately on the principle of contradiction. Indeed, language is an organ of perception, not simply a means of communication. J. Jaynes, (...) Origin of Consciousness. (shrink)

In this article I argue that "Timaeus" 48e-52d, the passage in which Plato introduces the receptacle into his ontology, Contains the material for a satisfactory response to the third man argument. Plato's use of "this" and "such" to distinguish the receptacle, Becoming, And the forms clarifies the nature of his ontology and indicates that the forms are not, In general, self-predicative. This result removes one argument against regarding the "Timaeus" as a late dialogue.

In (1991), Meinwald initiated a major change of direction in the study of Plato’s Parmenides and the Third Man Argument. On her conception of the Parmenides , Plato’s language systematically distinguishes two types or kinds of predication, namely, predications of the kind ‘x is F pros ta alla’ and ‘x is F pros heauto’. Intuitively speaking, the former is the common, everyday variety of predication, which holds when x is any object (perceptible object or Form) and F is a property (...) which x exemplifies or instantiates in the traditional sense. The latter is a special mode of predication which holds when x is a Form and F is a property which is, in some sense, part of the nature of that Form. Meinwald (1991, p. 75, footnote 18) traces the discovery of this distinction in Plato’s work to Frede (1967), who marks the distinction between pros allo and kath’ hauto predications by placing subscripts on the copula ‘is’. (shrink)

I am interested in examining the reasoning of Plato’s extremely condensed argument in Republic X for the uniqueness of Forms. I will explore the metaphysical principles and assumptions that are supplied in the text, or need to be presupposed in order to understand the reasoning in the argument. Further, I will reflect on the truth and philosophical significance of its conclusion.

Infinite regress arguments are part of a philosopher's tool kit of argumentation. But how sharp or strong is this tool? How effectively is it used? The typical presentation of infinite regress arguments throughout history is so succinct and has so many gaps that it is often unclear how an infinite regress is derived, and why an infinite regress is logically problematic, and as a result, it is often difficult to evaluate infinite regress arguments. These consequences of our customary way of (...) using this tool indicate that there is a need for a theory to re-orient our practice. My general approach to contribute to such a theory, consists of collecting and evaluating as many infinite regress arguments as possible, comparing and contrasting many of the formal and non-formal properties, looking for recurring patterns, and identifying the properties that appeared essential to those patterns. Two very general questions guided this work: How are infinite regresses generated in infinite regress arguments? How do infinite regresses logically function as premises in an argument? In answering these questions I clarify the notion of an infinite regress; identify different logical forms of infinite regresses; describe different kinds of infinite regress arguments; distinguish the rhetoric from the logic in infinite regress arguments; and suggest ways of improving our discussion and our practice of constructing and evaluating these arguments. (shrink)

Since the dawn of philosophy, the paradoxical interconnection between the continuous and the discrete plays a central rôle in attempts to understand the ontology of the world, while defying all attempts at consistent formulation. I investigate the relation between (classical) logic and concepts of “space” and “time” in physical and metaphysical theories, starting with the Greeks. An important part of my research consists in exploring the strong connections between paradoxes as they appear and are dealt with in ancient philosophy, and (...) their re-appearance in early modern natural philosophy, as well as in the foundations of contemporary science and mathematics. The way paradoxes are dealt with sheds light on a theory’s hidden metaphysical assumptions, especially with respect to matter, space, time and causation, it defines its ontological signature. This conclusion led me to the in-depth study of early modern natural philosophy, the origin of natural science, especially the influences ancient thinkers had on the new conceptions of space, time and causation developed by Newton, Huygens and Leibniz. (shrink)

This chapter discusses the first part of Aristotle's Posterior Analytics A-33, 88b30-89a10. I claim that Aristotle is not concerned with an epistemological distinction between knowledge and belief in general. He is rather making a contrast between scientific knowledge (which is equivalent to explanation by the primarily appropriate cause) and some explanatory beliefs that falls short of capturing the primarily appropriate cause.

This dissertation is a discussion of Wittgenstein's later philosophy. In it, Wittgenstein's answer to the "going on problem" will be presented: I will give his reply to the skeptic who denies that rule-following is possible. Chapter One will describe this problem. Chapter Two will give Wittgenstein's answer to it. Chapter Three will show how Wittgenstein used this answer to give the standards of mathematics. Chapter Four will compare Wittgenstein's answer to the going on problem to Plato's. Chapter Five will describe (...) Kant's influence on Wittgenstein's later philosophy. The leitmotif of these chapters will be that the way human beings apply a rule is the source of justification for its application. 1. (shrink)

An axiomatic theory of abstract objects is developed and used to construct models of Plato's Forms, Leibniz's Monads, Possible Worlds, Frege's Senses, stories, and fictional characters. The theory takes six primitive metaphysical notions: object ; n-place relations ,G,...); x,...x exemplify F x...x); x exists ; it is necessary that "); and x encodes F "). Properties and propositions are one place and zero place relations, respectively.objects are objects which necessarily fail to exist E!x"). The two most important proper axioms are (...) that no possibly existing object encodes any properties E!x F)xF)), and for every expressible condition on properties, there is an abstract object which encodes just the properties satisfying the condition x) )), where has no free x's). Semantically, an abstract object encodes a property iff the property is an element of the set of properties correlated with the object. Two abstract objects will be identical just in case they encode the same properties. Abstract objects may exemplify properties as well--being non-red, not having spatial location, etc. ;The models of Forms, Monads, and Possible Worlds consist in: identifying these philosophical entities as different species of abstract objects through definitions of the object language, and either showing that there are consequences of the theory which are reasonable facsimiles of assertions made by important philosophers or showing that there are many interesting theorems which capture our own intuitions about these entities . The model for Frege's Senses consists in: developing a language in which the abstract objects generated by the theory serve as the senses of names and descriptions, and showing that the data may be consistently translated into the language preserving truth. Finally, the model for fictional characters consists in: assigning abstract objects to serve as the denotations of names of stories and characters, and showing that such an assignment allows us to understand how the intuitively true sentences about stories and characters have the truth value that they do. ;The material is structured as follows. In Chapters I, III, and V, the elementary, modal, and typed theories of abstract objects are developed, respectively. In Chapters II, IV, and VI, these theories are applied, respectively. Each of the theoretical chapters is subdivided as follows: 1--The Language; 2--The Semantics; 3--The Logic; and 4--The Proper Axioms. Thus, the proper axioms of the theory are couched in a precisely defined and interpreted language, and the logic allow us to prove the consequences of the theory. (shrink)

A discussão nos livros dos Tópicos giram em torno dos debates dialéticos e seus elementos. Aristóteles discorre sobre os gêneros, as propriedades e os chamados acidentes e suas relações predicativas em categorias. Interessa-nos, sobretudo, compreender o papel desempenhado pela Definição e qual sua relação com os demais instrumentos para a dialética.